Quadratic Equations (Class 10 Mathematics)
Quadratic equations are polynomial equations of degree 2 and have numerous applications in physics and engineering. Solving them involves factorization, co
TL;DR: Quadratic equations are polynomial equations of degree 2 and have numerous applications in physics and engineering. Solving them involves factorizatio…
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
Quadratic equations are polynomial equations of degree 2 and have numerous applications in physics and engineering. Solving them involves factorization, co
Quadratic Equations MCQs with Answers & Explanations
Q1. The quadratic equation 2x^2 - 8x + 6 = 0 has roots:
- -1, -3
- 1, 3 ✓ (correct)
- 1, -3
- 2, 3
Explanation: Using the quadratic formula or factorization: 2x^2 - 8x + 6 = 2(x - 1)(x - 3) = 0, so roots are 1 and 3.
Q2. The discriminant of x^2 - 5x + 6 = 0 is:
- 25
- -24
- 1 ✓ (correct)
- 24
Explanation: D = b² - 4ac = (-5)² - 4(1)(6) = 25 - 24 = 1.
Q3. If the discriminant of a quadratic equation is negative, then the roots are:
- Real and equal
- Real and distinct
- No roots exist
- Complex and conjugates ✓ (correct)
Explanation: When the discriminant is negative, the roots are complex conjugates (non-real) and distinct from each other.
Q4. The sum of roots of 3x^2 + 5x - 2 = 0 is:
- -5/3 ✓ (correct)
- 5/3
- 2/3
- -2/3
Explanation: Sum of roots = -b/a = -5/3 for the quadratic equation ax^2 + bx + c = 0.
Q5. The product of roots of x^2 - 7x + 12 = 0 is:
- -12
- 12 ✓ (correct)
- -7
- 7
Explanation: Product of roots = c/a = 12/1 = 12 for the quadratic equation ax^2 + bx + c = 0.
Q6. The quadratic equation with roots 2 and -3 is:
- x^2 + x + 6 = 0
- x^2 - x - 6 = 0
- x^2 + x - 6 = 0 ✓ (correct)
- x^2 - x + 6 = 0
Explanation: If roots are 2 and -3, then equation is (x - 2)(x + 3) = 0, which gives x^2 + x - 6 = 0.
Q7. A quadratic equation has equal roots when its discriminant is:
- Undefined
- Negative
- Positive
- Zero ✓ (correct)
Explanation: A quadratic equation has real and equal roots when the discriminant equals zero.
Q8. The value of k for which x^2 - 4x + k = 0 has equal roots is:
- 4 ✓ (correct)
- 16
- 8
- 2
Explanation: For equal roots, discriminant = 0. So (-4)^2 - 4(1)(k) = 0, which gives 16 - 4k = 0, so k = 4.
Q9. The nature of roots of x^2 + x + 1 = 0 is:
- Real and unequal
- Complex conjugates ✓ (correct)
- Real and equal
- Real and distinct
Explanation: Discriminant = 1 - 4 = -3, which is negative, so roots are complex conjugates.
Q10. If the roots of ax^2 + bx + c = 0 are p and q, then the equation with roots 1/p and 1/q is:
- bx^2 + ax + c = 0
- ax^2 + bx + c = 0
- cx^2 + bx + a = 0 ✓ (correct)
- c + bx + ax^2 = 0
Explanation: If p and q are roots of ax^2 + bx + c = 0, then 1/p and 1/q are roots of cx^2 + bx + a = 0.
Frequently Asked Questions
What is the quadratic formula and when is it used?
The quadratic formula is x = (-b ± sqrt(b^2 - 4ac)) / 2a and is used when factorization is difficult or impossible.
How does the discriminant help determine the nature of roots?
The discriminant b^2 - 4ac determines if roots are real and distinct, real and equal, or complex conjugates.
More Class 10 Mathematics MCQs
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